[The Newell]

It's quite common for people to run a fridge via inverter while driving and the engine alternator can keep the batteries up, but less so when parked. You need an adequate battery bank for the wattage and even 400 watts is a lot at 12-13dcv. On a moderately warm day, the fridge will run most of the time, so that pretty much continuous at temps much above 70 degrees.

A new residential type fridge with a low energy compressor is actually more efficient if you wont to run in this fashion. Wattage is similar but the duty cycle less.